Quantitative strategies on High Frequency Data
submission of research project
Team members: Joanna Misiak and Agata Tomaszewska
Jan 20, 2026
Approaches undertaken
To find the best strategy we considered:
- two intersecting moving averages
- a single moving average and a selected volatility measure
For each approach we considered a trend following and mean reverting strategy. We tried pair-trading (both based on prices and returns) and portfolio based on the assets volatility. However, the best results were obtained with single asset trading.
We considered several combinations of parameters:
- slow and fast EMAs for two intersecting moving averages
- signal and slow EMAs for volatility breakout strategies
- volatilities and multipliers of the lower-upper thresholds for VB.
Approaches undertaken (cont’d)
For pair trading attempt, addtional filtering was applied. Filters based on correlation, cointegration and regression were applied, but none of them improved the overall results.
For the final, single asset trades, stop-loss condition was added. If the cumulative PnL for the day was lower than $500 and $1000, for group 1 and 2 respectively, trades for the day were stopped.
To find the best strategy, we looked at the sum of the final statistic for each quarter.
Finally selected strategy for group 1
As a result of the trial and error process, we have ended with volatility breakout model with momentum strategy for SP with signal and slow EMA of 30 and 240 respectively. The window length used in volatilities calculation was set to 120, while the multiplier for lower and upper threshold was set to 1. The stop-loss assumption was set as maximum of $500 loss per day.
Summary of results for group 1
| 2023_Q1 |
5.93 |
5.40 |
23710.55 |
21694.55 |
-1.00 |
4419995.25 |
2.58 |
15.06 |
| 2023_Q3 |
1.63 |
0.62 |
3277.05 |
1261.05 |
-1.27 |
-0.64 |
2.58 |
0.03 |
| 2023_Q4 |
3.19 |
2.51 |
9257.25 |
7337.25 |
387.65 |
78.32 |
2.50 |
4.01 |
| 2024_Q2 |
1.28 |
0.59 |
3809.35 |
1769.35 |
-1.06 |
-0.72 |
2.62 |
0.05 |
| 2024_Q4 |
3.46 |
2.65 |
8340.90 |
6444.90 |
127.49 |
61.33 |
2.43 |
4.01 |
| 2025_Q1 |
-0.12 |
-0.84 |
-324.65 |
-2316.65 |
-1.00 |
-1.45 |
2.63 |
-1.12 |
| 2025_Q2 |
3.15 |
2.82 |
18483.05 |
16587.05 |
-0.23 |
1928.65 |
2.43 |
6.53 |
The overall results look good - net Sharpe Ratio and net PnL is negative only for one quarter, Q1 2025. Net PnL is the highest for first and last analyzed quarter. Final statistics sum up to 28,57.
Equity line for group 1 – 2023Q1
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We can see that both gross and net cumulative PnL are rising. Small gap between the, indicating low costs.
Equity line for group 1 – 2023Q3
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More volatility can be observed - also bigger difference bewteen gross and net PnL. However, still positive PnL.
Equity line for group 1 – 2023Q4
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Rising trend of both gross and net PnL. Strategy behavior is consistent. A little divergence can be observed over time.
Equity line for group 1 – 2024Q2
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The start of the quarter was really good - gross and net PnL close together and rising quickly. However, the second half of the quarter it turned into losing startegy.
Equity line for group 1 – 2024Q4
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Strong, upward trend for both gross and net PnL. Final cumulative net PnL is lower than it could be - strong decrease in last couple of days.
Equity line for group 1 – 2025Q1
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Strongly volatile both gross and net PnL - mostly in the negative values. Not the best strategy for this quarter.
Equity line for group 1 – 2025Q2
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Sharp increase in first 15 days with low costs. Then stable for the rest of the quarter - strong final cumulative net PnL of more than $18,000.
Finally selected strategy for group 2
As a result of the trial and error process, we have ended with volatility breakout model with momentum strategy for XAG with signal and slow EMA of 30 and 240 respectively. The window length used in volatilities calculation was set to 60, while the multiplier for lower and upper threshold was set to 1. The stop-loss assumption was set as maximum of $1000 loss per day.
Summary of results for group 2
| 2023_Q1 |
2.06 |
1.84 |
14485.00 |
12985.00 |
6.38 |
5.82 |
1.92 |
3.44 |
| 2023_Q3 |
5.02 |
4.75 |
27830.00 |
26350.00 |
47.23 |
43.64 |
1.90 |
13.91 |
| 2023_Q4 |
2.61 |
2.37 |
15145.00 |
13745.00 |
10.20 |
8.98 |
1.79 |
4.90 |
| 2024_Q2 |
3.20 |
3.06 |
29715.00 |
28325.00 |
16.50 |
15.72 |
1.78 |
8.54 |
| 2024_Q4 |
2.17 |
2.03 |
19780.00 |
18440.00 |
11.89 |
11.18 |
1.70 |
4.46 |
| 2025_Q1 |
3.27 |
3.05 |
20970.00 |
19530.00 |
17.15 |
15.88 |
1.87 |
7.59 |
| 2025_Q2 |
2.54 |
2.39 |
23215.00 |
21815.00 |
9.69 |
9.00 |
1.79 |
5.83 |
The overall results look good - net Sharpe Ratio and net PnL is positive for all quarters. Average number of transaction is less than 2 trades per day. Final statistics sum up to 48,67.
Equity line for group 2 – 2023Q1
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Little volatility in the first half of the quarter. However, later steady, growing trend indicates profitable strategy.
Equity line for group 2 – 2023Q3
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Strategy started off strong - quick increase of both gross and net PnL. Little gap between gross and net PnL means low total transaction costs.
Equity line for group 2 – 2023Q4
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Slow start with balancing on the profitability edge. Later, followed by rapid increase and steady end of the quarter.
Equity line for group 2 – 2024Q2
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Steady increase in both gross and net PnL, indicating stable startegy. Little gap between the lines shows low total transaction costs (low trade number). Peak PnL at $30,000.
Equity line for group 2 – 2024Q4
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Strong, upward trade with little volatility. Gross and net PnL lines close togetger, indicating low tota transaction costs.
Equity line for group 2 – 2025Q1
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Strong, upward trend with high volatility in second half of the quarter. Ending culmulative net PnL strong at more that $20,000.
Equity line for group 2 – 2025Q2
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Highly volatile results - slow start with losing startegy in the middle of the period, turning into positive final cumulative net PnL. Slow growth of the gap between gross and net PnL.
Summary and conclusions
Overall results of the startegies are good. Both startegies ended up with positive statistic values for most of the quarters - 28 and 49 for group 1 and 2 respectively. The implementation of stop-loss condition had the biggest impact on the results, making the strategies profitable.
